pacman::p_load(olsrr, corrplot, ggpubr, sf, spdep,
GWmodel, tmap, tidyverse, gtsummary)Hands-on Exercise 11
Regression Modelling of Geographically Reference Data -Continuation
1.0 Setup
1.1 Installing R-Packages
R package for building OLS and performing diagnostics tests
R package for calibrating geographical weighted family of models
R package for multivariate data visualisation and analysis
Spatial data handling
- sf
Attribute data handling
- tidyverse, especially readr, ggplot2 and dplyr
Choropleth mapping
- tmap
1.2 Data Acquisition
Two data sets will be used:
URA Master Plansubzone boundary in shapefile format (i.e. MP14_SUBZONE_WEB_PL)condo_resale_2015: in csv format (i.e. condo_resale_2015.csv)
mpsz = st_read(dsn = "data/geospatial", layer = "MP14_SUBZONE_WEB_PL")Reading layer `MP14_SUBZONE_WEB_PL' from data source
`C:\Users\ngkng\Desktop\School\Geo -Local\Hands-on_Ex\Hands-on_Ex11\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21# Updating CRS info
mpsz_svy21 <- st_transform(mpsz, 3414)
st_crs(mpsz_svy21)Coordinate Reference System:
User input: EPSG:3414
wkt:
PROJCRS["SVY21 / Singapore TM",
BASEGEOGCRS["SVY21",
DATUM["SVY21",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
ID["EPSG",4757]],
CONVERSION["Singapore Transverse Mercator",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["northing (N)",north,
ORDER[1],
LENGTHUNIT["metre",1]],
AXIS["easting (E)",east,
ORDER[2],
LENGTHUNIT["metre",1]],
USAGE[
SCOPE["Cadastre, engineering survey, topographic mapping."],
AREA["Singapore - onshore and offshore."],
BBOX[1.13,103.59,1.47,104.07]],
ID["EPSG",3414]]st_bbox(mpsz_svy21) #view extent xmin ymin xmax ymax
2667.538 15748.721 56396.440 50256.334
Note
mpsz is a simple feature object [geometry type = multipolygon]
mpsz simple feature object does not have EPSG information
condo_resale.sp = read_rds("data/rds/condo_resale.sp")
condo_resale.res.sf = read_rds("data/rds/condo_resale.res.sf")2.0 Building Hedonic Pricing Models using GWmodel
2.1 Building Fixed Bandwidth GWR Model
bw.gwr() of GWModel package -> determine the optimal fixed bandwidth
adaptive = FALSE -> indicates interest in computing fixed bandwidth
To determine stopping rule:
CV -> Cross validation
AIC corrected
bw.fixed <- bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS +
FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sp,
approach="CV",
kernel="gaussian",
adaptive=FALSE,
longlat=FALSE)Fixed bandwidth: 17660.96 CV score: 8.259118e+14
Fixed bandwidth: 10917.26 CV score: 7.970454e+14
Fixed bandwidth: 6749.419 CV score: 7.273273e+14
Fixed bandwidth: 4173.553 CV score: 6.300006e+14
Fixed bandwidth: 2581.58 CV score: 5.404958e+14
Fixed bandwidth: 1597.687 CV score: 4.857515e+14
Fixed bandwidth: 989.6077 CV score: 4.722431e+14
Fixed bandwidth: 613.7939 CV score: 1.378294e+16
Fixed bandwidth: 1221.873 CV score: 4.778717e+14
Fixed bandwidth: 846.0596 CV score: 4.791629e+14
Fixed bandwidth: 1078.325 CV score: 4.751406e+14
Fixed bandwidth: 934.7772 CV score: 4.72518e+14
Fixed bandwidth: 1023.495 CV score: 4.730305e+14
Fixed bandwidth: 968.6643 CV score: 4.721317e+14
Fixed bandwidth: 955.7206 CV score: 4.722072e+14
Fixed bandwidth: 976.6639 CV score: 4.721387e+14
Fixed bandwidth: 963.7202 CV score: 4.721484e+14
Fixed bandwidth: 971.7199 CV score: 4.721293e+14
Fixed bandwidth: 973.6083 CV score: 4.721309e+14
Fixed bandwidth: 970.5527 CV score: 4.721295e+14
Fixed bandwidth: 972.4412 CV score: 4.721296e+14
Fixed bandwidth: 971.2741 CV score: 4.721292e+14
Fixed bandwidth: 970.9985 CV score: 4.721293e+14
Fixed bandwidth: 971.4443 CV score: 4.721292e+14
Fixed bandwidth: 971.5496 CV score: 4.721293e+14
Fixed bandwidth: 971.3793 CV score: 4.721292e+14
Fixed bandwidth: 971.3391 CV score: 4.721292e+14
Fixed bandwidth: 971.3143 CV score: 4.721292e+14
Fixed bandwidth: 971.3545 CV score: 4.721292e+14
Fixed bandwidth: 971.3296 CV score: 4.721292e+14
Fixed bandwidth: 971.345 CV score: 4.721292e+14
Fixed bandwidth: 971.3355 CV score: 4.721292e+14
Fixed bandwidth: 971.3413 CV score: 4.721292e+14
Fixed bandwidth: 971.3377 CV score: 4.721292e+14
Fixed bandwidth: 971.34 CV score: 4.721292e+14
Fixed bandwidth: 971.3405 CV score: 4.721292e+14
Fixed bandwidth: 971.3408 CV score: 4.721292e+14
Fixed bandwidth: 971.3403 CV score: 4.721292e+14
Fixed bandwidth: 971.3406 CV score: 4.721292e+14
Fixed bandwidth: 971.3404 CV score: 4.721292e+14
Fixed bandwidth: 971.3405 CV score: 4.721292e+14
Fixed bandwidth: 971.3405 CV score: 4.721292e+14
Note
The results shows that the recommended bandwidth is 971.3405 metres
Using fixed bandwidth & gaussian kernel
gwr.fixed <- gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS +
FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sp,
bw=bw.fixed,
kernel = 'gaussian',
longlat = FALSE)
gwr.fixed ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2024-11-02 00:54:18.275576
Call:
gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data = condo_resale.sp, bw = bw.fixed, kernel = "gaussian",
longlat = FALSE)
Dependent (y) variable: SELLING_PRICE
Independent variables: AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD
Number of data points: 1436
***********************************************************************
* Results of Global Regression *
***********************************************************************
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-3470778 -298119 -23481 248917 12234210
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 527633.22 108183.22 4.877 1.20e-06 ***
AREA_SQM 12777.52 367.48 34.771 < 2e-16 ***
AGE -24687.74 2754.84 -8.962 < 2e-16 ***
PROX_CBD -77131.32 5763.12 -13.384 < 2e-16 ***
PROX_CHILDCARE -318472.75 107959.51 -2.950 0.003231 **
PROX_ELDERLYCARE 185575.62 39901.86 4.651 3.61e-06 ***
PROX_URA_GROWTH_AREA 39163.25 11754.83 3.332 0.000885 ***
PROX_MRT -294745.11 56916.37 -5.179 2.56e-07 ***
PROX_PARK 570504.81 65507.03 8.709 < 2e-16 ***
PROX_PRIMARY_SCH 159856.14 60234.60 2.654 0.008046 **
PROX_SHOPPING_MALL -220947.25 36561.83 -6.043 1.93e-09 ***
PROX_BUS_STOP 682482.22 134513.24 5.074 4.42e-07 ***
NO_Of_UNITS -245.48 87.95 -2.791 0.005321 **
FAMILY_FRIENDLY 146307.58 46893.02 3.120 0.001845 **
FREEHOLD 350599.81 48506.48 7.228 7.98e-13 ***
---Significance stars
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 756000 on 1421 degrees of freedom
Multiple R-squared: 0.6507
Adjusted R-squared: 0.6472
F-statistic: 189.1 on 14 and 1421 DF, p-value: < 2.2e-16
***Extra Diagnostic information
Residual sum of squares: 8.120609e+14
Sigma(hat): 752522.9
AIC: 42966.76
AICc: 42967.14
BIC: 41731.39
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Fixed bandwidth: 971.3405
Regression points: the same locations as observations are used.
Distance metric: Euclidean distance metric is used.
****************Summary of GWR coefficient estimates:******************
Min. 1st Qu. Median 3rd Qu.
Intercept -3.5988e+07 -5.1998e+05 7.6780e+05 1.7412e+06
AREA_SQM 1.0003e+03 5.2758e+03 7.4740e+03 1.2301e+04
AGE -1.3475e+05 -2.0813e+04 -8.6260e+03 -3.7784e+03
PROX_CBD -7.7047e+07 -2.3608e+05 -8.3600e+04 3.4646e+04
PROX_CHILDCARE -6.0097e+06 -3.3667e+05 -9.7425e+04 2.9007e+05
PROX_ELDERLYCARE -3.5000e+06 -1.5970e+05 3.1971e+04 1.9577e+05
PROX_URA_GROWTH_AREA -3.0170e+06 -8.2013e+04 7.0749e+04 2.2612e+05
PROX_MRT -3.5282e+06 -6.5836e+05 -1.8833e+05 3.6922e+04
PROX_PARK -1.2062e+06 -2.1732e+05 3.5383e+04 4.1335e+05
PROX_PRIMARY_SCH -2.2695e+07 -1.7066e+05 4.8472e+04 5.1555e+05
PROX_SHOPPING_MALL -7.2585e+06 -1.6684e+05 -1.0517e+04 1.5923e+05
PROX_BUS_STOP -1.4676e+06 -4.5207e+04 3.7601e+05 1.1664e+06
NO_Of_UNITS -1.3170e+03 -2.4822e+02 -3.0846e+01 2.5496e+02
FAMILY_FRIENDLY -2.2749e+06 -1.1140e+05 7.6214e+03 1.6107e+05
FREEHOLD -9.2067e+06 3.8073e+04 1.5169e+05 3.7528e+05
Max.
Intercept 112793548
AREA_SQM 21575
AGE 434201
PROX_CBD 2704596
PROX_CHILDCARE 1654087
PROX_ELDERLYCARE 38867814
PROX_URA_GROWTH_AREA 78515730
PROX_MRT 3124316
PROX_PARK 18122425
PROX_PRIMARY_SCH 4637503
PROX_SHOPPING_MALL 1529952
PROX_BUS_STOP 11342182
NO_Of_UNITS 12907
FAMILY_FRIENDLY 1720744
FREEHOLD 6073636
************************Diagnostic information*************************
Number of data points: 1436
Effective number of parameters (2trace(S) - trace(S'S)): 438.3804
Effective degrees of freedom (n-2trace(S) + trace(S'S)): 997.6196
AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 42263.61
AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 41632.36
BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 42515.71
Residual sum of squares: 2.53407e+14
R-square value: 0.8909912
Adjusted R-square value: 0.8430417
***********************************************************************
Program stops at: 2024-11-02 00:54:19.005601
Note
The report shows that the AICc of the gwr is 42263.61 which is significantly smaller than the global multiple linear regression model of 42967.1.
2.2 Building Adaptive Bandwidth GWR Model
usage of bw.gwr() -> to determine the recommended data point to use
Similar to fixed bandwidth except adaptive = TRUE
bw.adaptive <- bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK +
PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sp,
approach="CV",
kernel="gaussian",
adaptive=TRUE,
longlat=FALSE)Adaptive bandwidth: 895 CV score: 7.952401e+14
Adaptive bandwidth: 561 CV score: 7.667364e+14
Adaptive bandwidth: 354 CV score: 6.953454e+14
Adaptive bandwidth: 226 CV score: 6.15223e+14
Adaptive bandwidth: 147 CV score: 5.674373e+14
Adaptive bandwidth: 98 CV score: 5.426745e+14
Adaptive bandwidth: 68 CV score: 5.168117e+14
Adaptive bandwidth: 49 CV score: 4.859631e+14
Adaptive bandwidth: 37 CV score: 4.646518e+14
Adaptive bandwidth: 30 CV score: 4.422088e+14
Adaptive bandwidth: 25 CV score: 4.430816e+14
Adaptive bandwidth: 32 CV score: 4.505602e+14
Adaptive bandwidth: 27 CV score: 4.462172e+14
Adaptive bandwidth: 30 CV score: 4.422088e+14
Note
The result shows that the 30 is the recommended data points to be used.
Using adaptive bandwidth & gaussian kernel
gwr.adaptive <- gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK +
PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sp, bw=bw.adaptive,
kernel = 'gaussian',
adaptive=TRUE,
longlat = FALSE)
gwr.adaptive ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2024-11-02 00:54:24.228502
Call:
gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data = condo_resale.sp, bw = bw.adaptive, kernel = "gaussian",
adaptive = TRUE, longlat = FALSE)
Dependent (y) variable: SELLING_PRICE
Independent variables: AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD
Number of data points: 1436
***********************************************************************
* Results of Global Regression *
***********************************************************************
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-3470778 -298119 -23481 248917 12234210
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 527633.22 108183.22 4.877 1.20e-06 ***
AREA_SQM 12777.52 367.48 34.771 < 2e-16 ***
AGE -24687.74 2754.84 -8.962 < 2e-16 ***
PROX_CBD -77131.32 5763.12 -13.384 < 2e-16 ***
PROX_CHILDCARE -318472.75 107959.51 -2.950 0.003231 **
PROX_ELDERLYCARE 185575.62 39901.86 4.651 3.61e-06 ***
PROX_URA_GROWTH_AREA 39163.25 11754.83 3.332 0.000885 ***
PROX_MRT -294745.11 56916.37 -5.179 2.56e-07 ***
PROX_PARK 570504.81 65507.03 8.709 < 2e-16 ***
PROX_PRIMARY_SCH 159856.14 60234.60 2.654 0.008046 **
PROX_SHOPPING_MALL -220947.25 36561.83 -6.043 1.93e-09 ***
PROX_BUS_STOP 682482.22 134513.24 5.074 4.42e-07 ***
NO_Of_UNITS -245.48 87.95 -2.791 0.005321 **
FAMILY_FRIENDLY 146307.58 46893.02 3.120 0.001845 **
FREEHOLD 350599.81 48506.48 7.228 7.98e-13 ***
---Significance stars
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 756000 on 1421 degrees of freedom
Multiple R-squared: 0.6507
Adjusted R-squared: 0.6472
F-statistic: 189.1 on 14 and 1421 DF, p-value: < 2.2e-16
***Extra Diagnostic information
Residual sum of squares: 8.120609e+14
Sigma(hat): 752522.9
AIC: 42966.76
AICc: 42967.14
BIC: 41731.39
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Adaptive bandwidth: 30 (number of nearest neighbours)
Regression points: the same locations as observations are used.
Distance metric: Euclidean distance metric is used.
****************Summary of GWR coefficient estimates:******************
Min. 1st Qu. Median 3rd Qu.
Intercept -1.3487e+08 -2.4669e+05 7.7928e+05 1.6194e+06
AREA_SQM 3.3188e+03 5.6285e+03 7.7825e+03 1.2738e+04
AGE -9.6746e+04 -2.9288e+04 -1.4043e+04 -5.6119e+03
PROX_CBD -2.5330e+06 -1.6256e+05 -7.7242e+04 2.6624e+03
PROX_CHILDCARE -1.2790e+06 -2.0175e+05 8.7158e+03 3.7778e+05
PROX_ELDERLYCARE -1.6212e+06 -9.2050e+04 6.1029e+04 2.8184e+05
PROX_URA_GROWTH_AREA -7.2686e+06 -3.0350e+04 4.5869e+04 2.4613e+05
PROX_MRT -4.3781e+07 -6.7282e+05 -2.2115e+05 -7.4593e+04
PROX_PARK -2.9020e+06 -1.6782e+05 1.1601e+05 4.6572e+05
PROX_PRIMARY_SCH -8.6418e+05 -1.6627e+05 -7.7853e+03 4.3222e+05
PROX_SHOPPING_MALL -1.8272e+06 -1.3175e+05 -1.4049e+04 1.3799e+05
PROX_BUS_STOP -2.0579e+06 -7.1461e+04 4.1104e+05 1.2071e+06
NO_Of_UNITS -2.1993e+03 -2.3685e+02 -3.4699e+01 1.1657e+02
FAMILY_FRIENDLY -5.9879e+05 -5.0927e+04 2.6173e+04 2.2481e+05
FREEHOLD -1.6340e+05 4.0765e+04 1.9023e+05 3.7960e+05
Max.
Intercept 18758355
AREA_SQM 23064
AGE 13303
PROX_CBD 11346650
PROX_CHILDCARE 2892127
PROX_ELDERLYCARE 2465671
PROX_URA_GROWTH_AREA 7384059
PROX_MRT 1186242
PROX_PARK 2588497
PROX_PRIMARY_SCH 3381462
PROX_SHOPPING_MALL 38038564
PROX_BUS_STOP 12081592
NO_Of_UNITS 1010
FAMILY_FRIENDLY 2072414
FREEHOLD 1813995
************************Diagnostic information*************************
Number of data points: 1436
Effective number of parameters (2trace(S) - trace(S'S)): 350.3088
Effective degrees of freedom (n-2trace(S) + trace(S'S)): 1085.691
AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 41982.22
AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 41546.74
BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 41914.08
Residual sum of squares: 2.528227e+14
R-square value: 0.8912425
Adjusted R-square value: 0.8561185
***********************************************************************
Program stops at: 2024-11-02 00:54:25.083132
Note
The report shows that the AICc the adaptive distance gwr is 41982.22 which is even smaller than the AICc of the fixed distance gwr of 42263.61.
2.3 Visualising GWR output
In addition to regression residuals, the output feature class table includes fields for observed and predicted y values, condition number (cond), Local R2, residuals, and explanatory variable coefficients and standard errors:
Condition Number: this diagnostic evaluates local collinearity. In the presence of strong local collinearity, results become unstable. Results associated with condition numbers larger than 30, may be unreliable.
Local R2: these values range between 0.0 and 1.0 and indicate how well the local regression model fits observed y values. Very low values indicate the local model is performing poorly. Mapping the Local R2 values to see where GWR predicts well and where it predicts poorly may provide clues about important variables that may be missing from the regression model.
Predicted: these are the estimated (or fitted) y values 3. computed by GWR.
Residuals: to obtain the residual values, the fitted y values are subtracted from the observed y values. Standardized residuals have a mean of zero and a standard deviation of 1. A cold-to-hot rendered map of standardized residuals can be produce by using these values.
Coefficient Standard Error: these values measure the reliability of each coefficient estimate. Confidence in those estimates are higher when standard errors are small in relation to the actual coefficient values. Large standard errors may indicate problems with local collinearity.
They are all stored in a SpatialPointsDataFrame or SpatialPolygonsDataFrame object integrated with fit.points, GWR coefficient estimates, y value, predicted values, coefficient standard errors and t-values in its “data” slot in an object called SDF of the output list.
# Converting SDF into sf data.frame
condo_resale.sf.adaptive <- st_as_sf(gwr.adaptive$SDF) %>%
st_transform(crs=3414)
condo_resale.sf.adaptive.svy21 <- st_transform(condo_resale.sf.adaptive, 3414)
condo_resale.sf.adaptive.svy21 Simple feature collection with 1436 features and 51 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 14940.85 ymin: 24765.67 xmax: 43352.45 ymax: 48382.81
Projected CRS: SVY21 / Singapore TM
First 10 features:
Intercept AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE
1 2050011.7 9561.892 -9514.634 -120681.9 319266.92 -393417.79
2 1633128.2 16576.853 -58185.479 -149434.2 441102.18 325188.74
3 3433608.2 13091.861 -26707.386 -259397.8 -120116.82 535855.81
4 234358.9 20730.601 -93308.988 2426853.7 480825.28 314783.72
5 2285804.9 6722.836 -17608.018 -316835.5 90764.78 -137384.61
6 -3568877.4 6039.581 -26535.592 327306.1 -152531.19 -700392.85
7 -2874842.4 16843.575 -59166.727 -983577.2 -177810.50 -122384.02
8 2038086.0 6905.135 -17681.897 -285076.6 70259.40 -96012.78
9 1718478.4 9580.703 -14401.128 105803.4 -657698.02 -123276.00
10 3457054.0 14072.011 -31579.884 -234895.4 79961.45 548581.04
PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH
1 -159980.20 -299742.96 -172104.47 242668.03
2 -142290.39 -2510522.23 523379.72 1106830.66
3 -253621.21 -936853.28 209099.85 571462.33
4 -2679297.89 -2039479.50 -759153.26 3127477.21
5 303714.81 -44567.05 -10284.62 30413.56
6 -28051.25 733566.47 1511488.92 320878.23
7 1397676.38 -2745430.34 710114.74 1786570.95
8 269368.71 -14552.99 73533.34 53359.73
9 -361974.72 -476785.32 -132067.59 -40128.92
10 -150024.38 -1503835.53 574155.47 108996.67
PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD
1 300881.390 1210615.4 104.8290640 -9075.370 303955.6
2 -87693.378 1843587.2 -288.3441183 310074.664 396221.3
3 -126732.712 1411924.9 -9.5532945 5949.746 168821.7
4 -29593.342 7225577.5 -161.3551620 1556178.531 1212515.6
5 -7490.586 677577.0 42.2659674 58986.951 328175.2
6 258583.881 1086012.6 -214.3671271 201992.641 471873.1
7 -384251.210 5094060.5 -0.9212521 359659.512 408871.9
8 -39634.902 735767.1 30.1741069 55602.506 347075.0
9 276718.757 2815772.4 675.1615559 -30453.297 503872.8
10 -454726.822 2123557.0 -21.3044311 -100935.586 213324.6
y yhat residual CV_Score Stud_residual Intercept_SE AREA_SQM_SE
1 3000000 2886532 113468.16 0 0.38207013 516105.5 823.2860
2 3880000 3466801 413198.52 0 1.01433140 488083.5 825.2380
3 3325000 3616527 -291527.20 0 -0.83780678 963711.4 988.2240
4 4250000 5435482 -1185481.63 0 -2.84614670 444185.5 617.4007
5 1400000 1388166 11834.26 0 0.03404453 2119620.6 1376.2778
6 1320000 1516702 -196701.94 0 -0.72065800 28572883.7 2348.0091
7 3410000 3266881 143118.77 0 0.41291992 679546.6 893.5893
8 1420000 1431955 -11955.27 0 -0.03033109 2217773.1 1415.2604
9 2025000 1832799 192200.83 0 0.52018109 814281.8 943.8434
10 2550000 2223364 326635.53 0 1.10559735 2410252.0 1271.4073
AGE_SE PROX_CBD_SE PROX_CHILDCARE_SE PROX_ELDERLYCARE_SE
1 5889.782 37411.22 319111.1 120633.34
2 6226.916 23615.06 299705.3 84546.69
3 6510.236 56103.77 349128.5 129687.07
4 6010.511 469337.41 304965.2 127150.69
5 8180.361 410644.47 698720.6 327371.55
6 14601.909 5272846.47 1141599.8 1653002.19
7 8970.629 346164.20 530101.1 148598.71
8 8661.309 438035.69 742532.8 399221.05
9 11791.208 89148.35 704630.7 329683.30
10 9941.980 173532.77 500976.2 281876.74
PROX_URA_GROWTH_AREA_SE PROX_MRT_SE PROX_PARK_SE PROX_PRIMARY_SCH_SE
1 56207.39 185181.3 205499.6 152400.7
2 76956.50 281133.9 229358.7 165150.7
3 95774.60 275483.7 314124.3 196662.6
4 470762.12 279877.1 227249.4 240878.9
5 474339.56 363830.0 364580.9 249087.7
6 5496627.21 730453.2 1741712.0 683265.5
7 371692.97 375511.9 297400.9 344602.8
8 517977.91 423155.4 440984.4 261251.2
9 153436.22 285325.4 304998.4 278258.5
10 239182.57 571355.7 599131.8 331284.8
PROX_SHOPPING_MALL_SE PROX_BUS_STOP_SE NO_Of_UNITS_SE FAMILY_FRIENDLY_SE
1 109268.8 600668.6 218.1258 131474.7
2 98906.8 410222.1 208.9410 114989.1
3 119913.3 464156.7 210.9828 146607.2
4 177104.1 562810.8 361.7767 108726.6
5 301032.9 740922.4 299.5034 160663.7
6 2931208.6 1418333.3 602.5571 331727.0
7 249969.5 821236.4 532.1978 129241.2
8 351634.0 775038.4 338.6777 171895.1
9 289872.7 850095.5 439.9037 220223.4
10 265529.7 631399.2 259.0169 189125.5
FREEHOLD_SE Intercept_TV AREA_SQM_TV AGE_TV PROX_CBD_TV
1 115954.0 3.9720784 11.614302 -1.615447 -3.22582173
2 130110.0 3.3460017 20.087361 -9.344188 -6.32792021
3 141031.5 3.5629010 13.247868 -4.102368 -4.62353528
4 138239.1 0.5276150 33.577223 -15.524302 5.17080808
5 210641.1 1.0784029 4.884795 -2.152474 -0.77155660
6 374347.3 -0.1249043 2.572214 -1.817269 0.06207388
7 182216.9 -4.2305303 18.849348 -6.595605 -2.84136028
8 216649.4 0.9189786 4.879056 -2.041481 -0.65080678
9 220473.7 2.1104224 10.150733 -1.221345 1.18682383
10 206346.2 1.4343123 11.068059 -3.176418 -1.35360852
PROX_CHILDCARE_TV PROX_ELDERLYCARE_TV PROX_URA_GROWTH_AREA_TV PROX_MRT_TV
1 1.00048819 -3.2612693 -2.846248368 -1.61864578
2 1.47178634 3.8462625 -1.848971738 -8.92998600
3 -0.34404755 4.1319138 -2.648105057 -3.40075727
4 1.57665606 2.4756745 -5.691404992 -7.28705261
5 0.12990138 -0.4196596 0.640289855 -0.12249416
6 -0.13361179 -0.4237096 -0.005103357 1.00426206
7 -0.33542751 -0.8235874 3.760298131 -7.31116712
8 0.09462126 -0.2405003 0.520038994 -0.03439159
9 -0.93339393 -0.3739225 -2.359121712 -1.67102293
10 0.15961128 1.9461735 -0.627237944 -2.63204802
PROX_PARK_TV PROX_PRIMARY_SCH_TV PROX_SHOPPING_MALL_TV PROX_BUS_STOP_TV
1 -0.83749312 1.5923022 2.75358842 2.0154464
2 2.28192684 6.7019454 -0.88662640 4.4941192
3 0.66565951 2.9058009 -1.05686949 3.0419145
4 -3.34061770 12.9836105 -0.16709578 12.8383775
5 -0.02820944 0.1220998 -0.02488294 0.9145046
6 0.86781794 0.4696245 0.08821750 0.7656963
7 2.38773567 5.1844351 -1.53719231 6.2029165
8 0.16674816 0.2042469 -0.11271635 0.9493299
9 -0.43301073 -0.1442145 0.95462153 3.3123012
10 0.95831249 0.3290120 -1.71252687 3.3632555
NO_Of_UNITS_TV FAMILY_FRIENDLY_TV FREEHOLD_TV Local_R2
1 0.480589953 -0.06902748 2.621347 0.8846744
2 -1.380026395 2.69655779 3.045280 0.8899773
3 -0.045279967 0.04058290 1.197050 0.8947007
4 -0.446007570 14.31276425 8.771149 0.9073605
5 0.141120178 0.36714544 1.557983 0.9510057
6 -0.355762335 0.60891234 1.260522 0.9247586
7 -0.001731033 2.78285441 2.243875 0.8310458
8 0.089093858 0.32346758 1.602012 0.9463936
9 1.534793921 -0.13828365 2.285410 0.8380365
10 -0.082251138 -0.53369623 1.033819 0.9080753
geometry
1 POINT (22085.12 29951.54)
2 POINT (25656.84 34546.2)
3 POINT (23963.99 32890.8)
4 POINT (27044.28 32319.77)
5 POINT (41042.56 33743.64)
6 POINT (39717.04 32943.1)
7 POINT (28419.1 33513.37)
8 POINT (40763.57 33879.61)
9 POINT (23595.63 28884.78)
10 POINT (24586.56 33194.31)gwr.adaptive.output <- as.data.frame(gwr.adaptive$SDF)
condo_resale.sf.adaptive <- cbind(condo_resale.res.sf, as.matrix(gwr.adaptive.output))
glimpse(condo_resale.sf.adaptive)Rows: 1,436
Columns: 77
$ POSTCODE <dbl> 118635, 288420, 267833, 258380, 467169, 466472…
$ SELLING_PRICE <dbl> 3000000, 3880000, 3325000, 4250000, 1400000, 1…
$ AREA_SQM <dbl> 309, 290, 248, 127, 145, 139, 218, 141, 165, 1…
$ AGE <dbl> 30, 32, 33, 7, 28, 22, 24, 24, 27, 31, 17, 22,…
$ PROX_CBD <dbl> 7.941259, 6.609797, 6.898000, 4.038861, 11.783…
$ PROX_CHILDCARE <dbl> 0.16597932, 0.28027246, 0.42922669, 0.39473543…
$ PROX_ELDERLYCARE <dbl> 2.5198118, 1.9333338, 0.5021395, 1.9910316, 1.…
$ PROX_URA_GROWTH_AREA <dbl> 6.618741, 7.505109, 6.463887, 4.906512, 6.4106…
$ PROX_HAWKER_MARKET <dbl> 1.76542207, 0.54507614, 0.37789301, 1.68259969…
$ PROX_KINDERGARTEN <dbl> 0.05835552, 0.61592412, 0.14120309, 0.38200076…
$ PROX_MRT <dbl> 0.5607188, 0.6584461, 0.3053433, 0.6910183, 0.…
$ PROX_PARK <dbl> 1.1710446, 0.1992269, 0.2779886, 0.9832843, 0.…
$ PROX_PRIMARY_SCH <dbl> 1.6340256, 0.9747834, 1.4715016, 1.4546324, 0.…
$ PROX_TOP_PRIMARY_SCH <dbl> 3.3273195, 0.9747834, 1.4715016, 2.3006394, 0.…
$ PROX_SHOPPING_MALL <dbl> 2.2102717, 2.9374279, 1.2256850, 0.3525671, 1.…
$ PROX_SUPERMARKET <dbl> 0.9103958, 0.5900617, 0.4135583, 0.4162219, 0.…
$ PROX_BUS_STOP <dbl> 0.10336166, 0.28673408, 0.28504777, 0.29872340…
$ NO_Of_UNITS <dbl> 18, 20, 27, 30, 30, 31, 32, 32, 32, 32, 34, 34…
$ FAMILY_FRIENDLY <dbl> 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0…
$ FREEHOLD <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1…
$ LEASEHOLD_99YR <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ LOG_SELLING_PRICE <dbl> 14.91412, 15.17135, 15.01698, 15.26243, 14.151…
$ MLR_RES <dbl> -1489099.55, 415494.57, 194129.69, 1088992.71,…
$ Intercept <dbl> 2050011.67, 1633128.24, 3433608.17, 234358.91,…
$ AREA_SQM.1 <dbl> 9561.892, 16576.853, 13091.861, 20730.601, 672…
$ AGE.1 <dbl> -9514.634, -58185.479, -26707.386, -93308.988,…
$ PROX_CBD.1 <dbl> -120681.94, -149434.22, -259397.77, 2426853.66…
$ PROX_CHILDCARE.1 <dbl> 319266.925, 441102.177, -120116.816, 480825.28…
$ PROX_ELDERLYCARE.1 <dbl> -393417.795, 325188.741, 535855.806, 314783.72…
$ PROX_URA_GROWTH_AREA.1 <dbl> -159980.203, -142290.389, -253621.206, -267929…
$ PROX_MRT.1 <dbl> -299742.96, -2510522.23, -936853.28, -2039479.…
$ PROX_PARK.1 <dbl> -172104.47, 523379.72, 209099.85, -759153.26, …
$ PROX_PRIMARY_SCH.1 <dbl> 242668.03, 1106830.66, 571462.33, 3127477.21, …
$ PROX_SHOPPING_MALL.1 <dbl> 300881.390, -87693.378, -126732.712, -29593.34…
$ PROX_BUS_STOP.1 <dbl> 1210615.44, 1843587.22, 1411924.90, 7225577.51…
$ NO_Of_UNITS.1 <dbl> 104.8290640, -288.3441183, -9.5532945, -161.35…
$ FAMILY_FRIENDLY.1 <dbl> -9075.370, 310074.664, 5949.746, 1556178.531, …
$ FREEHOLD.1 <dbl> 303955.61, 396221.27, 168821.75, 1212515.58, 3…
$ y <dbl> 3000000, 3880000, 3325000, 4250000, 1400000, 1…
$ yhat <dbl> 2886531.8, 3466801.5, 3616527.2, 5435481.6, 13…
$ residual <dbl> 113468.16, 413198.52, -291527.20, -1185481.63,…
$ CV_Score <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ Stud_residual <dbl> 0.38207013, 1.01433140, -0.83780678, -2.846146…
$ Intercept_SE <dbl> 516105.5, 488083.5, 963711.4, 444185.5, 211962…
$ AREA_SQM_SE <dbl> 823.2860, 825.2380, 988.2240, 617.4007, 1376.2…
$ AGE_SE <dbl> 5889.782, 6226.916, 6510.236, 6010.511, 8180.3…
$ PROX_CBD_SE <dbl> 37411.22, 23615.06, 56103.77, 469337.41, 41064…
$ PROX_CHILDCARE_SE <dbl> 319111.1, 299705.3, 349128.5, 304965.2, 698720…
$ PROX_ELDERLYCARE_SE <dbl> 120633.34, 84546.69, 129687.07, 127150.69, 327…
$ PROX_URA_GROWTH_AREA_SE <dbl> 56207.39, 76956.50, 95774.60, 470762.12, 47433…
$ PROX_MRT_SE <dbl> 185181.3, 281133.9, 275483.7, 279877.1, 363830…
$ PROX_PARK_SE <dbl> 205499.6, 229358.7, 314124.3, 227249.4, 364580…
$ PROX_PRIMARY_SCH_SE <dbl> 152400.7, 165150.7, 196662.6, 240878.9, 249087…
$ PROX_SHOPPING_MALL_SE <dbl> 109268.8, 98906.8, 119913.3, 177104.1, 301032.…
$ PROX_BUS_STOP_SE <dbl> 600668.6, 410222.1, 464156.7, 562810.8, 740922…
$ NO_Of_UNITS_SE <dbl> 218.1258, 208.9410, 210.9828, 361.7767, 299.50…
$ FAMILY_FRIENDLY_SE <dbl> 131474.73, 114989.07, 146607.22, 108726.62, 16…
$ FREEHOLD_SE <dbl> 115954.0, 130110.0, 141031.5, 138239.1, 210641…
$ Intercept_TV <dbl> 3.9720784, 3.3460017, 3.5629010, 0.5276150, 1.…
$ AREA_SQM_TV <dbl> 11.614302, 20.087361, 13.247868, 33.577223, 4.…
$ AGE_TV <dbl> -1.6154474, -9.3441881, -4.1023685, -15.524301…
$ PROX_CBD_TV <dbl> -3.22582173, -6.32792021, -4.62353528, 5.17080…
$ PROX_CHILDCARE_TV <dbl> 1.000488185, 1.471786337, -0.344047555, 1.5766…
$ PROX_ELDERLYCARE_TV <dbl> -3.26126929, 3.84626245, 4.13191383, 2.4756745…
$ PROX_URA_GROWTH_AREA_TV <dbl> -2.846248368, -1.848971738, -2.648105057, -5.6…
$ PROX_MRT_TV <dbl> -1.61864578, -8.92998600, -3.40075727, -7.2870…
$ PROX_PARK_TV <dbl> -0.83749312, 2.28192684, 0.66565951, -3.340617…
$ PROX_PRIMARY_SCH_TV <dbl> 1.59230221, 6.70194543, 2.90580089, 12.9836104…
$ PROX_SHOPPING_MALL_TV <dbl> 2.753588422, -0.886626400, -1.056869486, -0.16…
$ PROX_BUS_STOP_TV <dbl> 2.0154464, 4.4941192, 3.0419145, 12.8383775, 0…
$ NO_Of_UNITS_TV <dbl> 0.480589953, -1.380026395, -0.045279967, -0.44…
$ FAMILY_FRIENDLY_TV <dbl> -0.06902748, 2.69655779, 0.04058290, 14.312764…
$ FREEHOLD_TV <dbl> 2.6213469, 3.0452799, 1.1970499, 8.7711485, 1.…
$ Local_R2 <dbl> 0.8846744, 0.8899773, 0.8947007, 0.9073605, 0.…
$ coords.x1 <dbl> 22085.12, 25656.84, 23963.99, 27044.28, 41042.…
$ coords.x2 <dbl> 29951.54, 34546.20, 32890.80, 32319.77, 33743.…
$ geometry <POINT [m]> POINT (22085.12 29951.54), POINT (25656.…summary(gwr.adaptive$SDF$yhat) Min. 1st Qu. Median Mean 3rd Qu. Max.
171347 1102001 1385528 1751842 1982307 13887901 # Set tmap options to check and fix any invalid polygons
tmap_options(check.and.fix = TRUE)
tmap_mode("view")tmap mode set to interactive viewingtm_shape(mpsz_svy21)+
tm_polygons(alpha = 0.1) +
tm_shape(condo_resale.sf.adaptive) +
tm_dots(col = "Local_R2",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(11,14))Warning: The shape mpsz_svy21 is invalid (after reprojection). See
sf::st_is_validtmap_mode("plot")tmap mode set to plottingtmap_mode("view")tmap mode set to interactive viewingAREA_SQM_SE <- tm_shape(mpsz_svy21)+
tm_polygons(alpha = 0.1) +
tm_shape(condo_resale.sf.adaptive) +
tm_dots(col = "AREA_SQM_SE",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(11,14))
AREA_SQM_TV <- tm_shape(mpsz_svy21)+
tm_polygons(alpha = 0.1) +
tm_shape(condo_resale.sf.adaptive) +
tm_dots(col = "AREA_SQM_TV",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(11,14))
tmap_arrange(AREA_SQM_SE, AREA_SQM_TV,
asp=1, ncol=2,
sync = TRUE)Warning: The shape mpsz_svy21 is invalid (after reprojection). See
sf::st_is_valid
Warning: The shape mpsz_svy21 is invalid (after reprojection). See
sf::st_is_valid